{
  "id": "1612.03282",
  "version": "v1",
  "published": "2016-12-10T11:47:36.000Z",
  "updated": "2016-12-10T11:47:36.000Z",
  "title": "Some remarks on derivations on the algebra of operators in Hilbert pro-C*-bimodules",
  "authors": [
    "Khadijeh Karimi",
    "Kamran Sharifi"
  ],
  "comment": "8 pages, accepted",
  "categories": [
    "math.OA"
  ],
  "abstract": "Suppose $A$ is a pro-C*-algebra. Let $L_{A}(E)$ be the pro-C*-algebra of adjointable operators on a Hilbert $A$-module $E$ and let $K_{A}(E)$ be the closed two sided $*$-ideal of all compact operators on $E$. We prove that if $E$ be a full Hilbert $A$-module, the innerness of derivations on $K_{A}(E)$ implies the innerness of derivations on $L_{A}(E)$. We show that if $A$ is a commutative pro-C*-algebra and $E$ is a Hilbert $A$-bimodule then every derivation on $K_{A}(E)$ is zero. Moreover, if $A$ is a commutative $\\sigma$-C*-algebra and $E$ is a Hilbert $A$-bimodule then every derivation on $L_{A}(E)$ is zero, too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-10T11:47:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L08",
      "46L05",
      "46H25",
      "47B47"
    ],
    "keywords": [
      "derivation",
      "compact operators",
      "full hilbert",
      "adjointable operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}